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<FONT color="green">001</FONT>    package gates;<a name="line.1"></a>
<FONT color="green">002</FONT>    <a name="line.2"></a>
<FONT color="green">003</FONT>    import register.Register;<a name="line.3"></a>
<FONT color="green">004</FONT>    import mathtools.*;<a name="line.4"></a>
<FONT color="green">005</FONT>    import gates.MatrixGate;<a name="line.5"></a>
<FONT color="green">006</FONT>    import exceptions.noQubitException;<a name="line.6"></a>
<FONT color="green">007</FONT>    <a name="line.7"></a>
<FONT color="green">008</FONT>    /**<a name="line.8"></a>
<FONT color="green">009</FONT>     * &lt;p&gt;Cnot Gate in Matrix Representation for specific Control and Target Qubits.&lt;/p&gt;<a name="line.9"></a>
<FONT color="green">010</FONT>     * &lt;p&gt;The Gate is constructed by the addition of two matrices, A &amp; B. Each matrix depends<a name="line.10"></a>
<FONT color="green">011</FONT>     * on a combination of an outer product and the 2x2 identity matrix and a 2x2 Not <a name="line.11"></a>
<FONT color="green">012</FONT>     * matrix. The number of operations for each of the matrices is proportional to <a name="line.12"></a>
<FONT color="green">013</FONT>     * the number of Qubits in the Register. The matrix A has a total of (N-1)<a name="line.13"></a>
<FONT color="green">014</FONT>     * tensor product operations of the 2x2 Identity matrix, where N is the number<a name="line.14"></a>
<FONT color="green">015</FONT>     * of Qubits in the Register, and one operation of the outer product of two<a name="line.15"></a>
<FONT color="green">016</FONT>     * one Qubit states. Ie. The outer product of |0&gt;&lt;0|. The position of the outer<a name="line.16"></a>
<FONT color="green">017</FONT>     * product is dependent on the specified Control bit of the Gate. The matrix B<a name="line.17"></a>
<FONT color="green">018</FONT>     * has a total of (N-2) Identity operations with an outer product operation and<a name="line.18"></a>
<FONT color="green">019</FONT>     * a Not operation. The outer product for matrix B is |1&gt;&lt;1|, and the position<a name="line.19"></a>
<FONT color="green">020</FONT>     * is the same as for matrix A. The position of the Not operation is dependent<a name="line.20"></a>
<FONT color="green">021</FONT>     * on the specified position of the target Qubit. The Cnot matrix is then the <a name="line.21"></a>
<FONT color="green">022</FONT>     * addition of matrices A and B. &lt;/p&gt;<a name="line.22"></a>
<FONT color="green">023</FONT>     * &lt;p&gt;For example the Cnot applied to a 4 Qubit Register(Qubits 0,1,2 and 3)<a name="line.23"></a>
<FONT color="green">024</FONT>     *  with Control bit 1 and target 2 would become:&lt;br /&gt;<a name="line.24"></a>
<FONT color="green">025</FONT>     *  A = I x |0&gt;&lt;0| x I x I &lt;br /&gt;<a name="line.25"></a>
<FONT color="green">026</FONT>     *  B = I x |1&gt;&lt;1| x Not x I &lt;br /&gt;<a name="line.26"></a>
<FONT color="green">027</FONT>     *  Cnot = A + B&lt;br /&gt;<a name="line.27"></a>
<FONT color="green">028</FONT>     *  Where x represents the Tensor Product, A and B are two construction matrices,<a name="line.28"></a>
<FONT color="green">029</FONT>     *  I is the 2x2 Identity matrix, |0&gt;&lt;0| and |1&gt;&lt;1| are the two outer products and <a name="line.29"></a>
<FONT color="green">030</FONT>     *  Not is a 2x2 inversion matrix (0-&gt;1 and 1-&gt;0).&lt;/p&gt;<a name="line.30"></a>
<FONT color="green">031</FONT>     * @author Richard Inskip, Jan Zaucha<a name="line.31"></a>
<FONT color="green">032</FONT>     *<a name="line.32"></a>
<FONT color="green">033</FONT>     */<a name="line.33"></a>
<FONT color="green">034</FONT>    public class CnotMatrix extends MatrixGate {<a name="line.34"></a>
<FONT color="green">035</FONT>    <a name="line.35"></a>
<FONT color="green">036</FONT>            /* I2 - Identity matrix 2x2<a name="line.36"></a>
<FONT color="green">037</FONT>             * Not - 2x2 Not matrix :       |0 1|<a name="line.37"></a>
<FONT color="green">038</FONT>             *                                                      |1 0|<a name="line.38"></a>
<FONT color="green">039</FONT>             * outer_0 and outer_1 is the Outer Product (tensor product for vectors)<a name="line.39"></a>
<FONT color="green">040</FONT>             * outer_0:     |1 0|<a name="line.40"></a>
<FONT color="green">041</FONT>             *                      |0 0|<a name="line.41"></a>
<FONT color="green">042</FONT>             * outer_1      |0 0|<a name="line.42"></a>
<FONT color="green">043</FONT>             *                      |0 1|<a name="line.43"></a>
<FONT color="green">044</FONT>             * Variables LHS/RHS are two matrices in which we use as running counters to<a name="line.44"></a>
<FONT color="green">045</FONT>             * finally add them together.<a name="line.45"></a>
<FONT color="green">046</FONT>             * num1 is a complex number representation of integer 1<a name="line.46"></a>
<FONT color="green">047</FONT>             * Set ctrl and target to be accessible globally within the Class<a name="line.47"></a>
<FONT color="green">048</FONT>             */<a name="line.48"></a>
<FONT color="green">049</FONT>            /** Store the target qubit the gate acts on*/   <a name="line.49"></a>
<FONT color="green">050</FONT>            private int target;<a name="line.50"></a>
<FONT color="green">051</FONT>            /** Store the control qubit the gate acts on*/  <a name="line.51"></a>
<FONT color="green">052</FONT>            private int ctrl;<a name="line.52"></a>
<FONT color="green">053</FONT>            /** Store a 2x2 identity matrix */<a name="line.53"></a>
<FONT color="green">054</FONT>            private Matrix I2 = Matrix.IdentityMatrix(2);<a name="line.54"></a>
<FONT color="green">055</FONT>            /** Stores a 2x2 not gate in matrix form */<a name="line.55"></a>
<FONT color="green">056</FONT>            private Matrix Not;<a name="line.56"></a>
<FONT color="green">057</FONT>            /** Matrix needed to construct the cnot matrix */<a name="line.57"></a>
<FONT color="green">058</FONT>            private Matrix outer_0;<a name="line.58"></a>
<FONT color="green">059</FONT>            /** Matrix needed to construct the cnot matrix */<a name="line.59"></a>
<FONT color="green">060</FONT>            private Matrix outer_1;<a name="line.60"></a>
<FONT color="green">061</FONT>            /** Matrix needed to construct the cnot matrix */<a name="line.61"></a>
<FONT color="green">062</FONT>            private Matrix LHS;<a name="line.62"></a>
<FONT color="green">063</FONT>            /** Matrix needed to construct the cnot matrix */<a name="line.63"></a>
<FONT color="green">064</FONT>            private Matrix RHS;<a name="line.64"></a>
<FONT color="green">065</FONT>            /** Complex number 1+0i needed to set elements on the matrices */<a name="line.65"></a>
<FONT color="green">066</FONT>            private Complex num1;<a name="line.66"></a>
<FONT color="green">067</FONT>            <a name="line.67"></a>
<FONT color="green">068</FONT>    <a name="line.68"></a>
<FONT color="green">069</FONT>            /**<a name="line.69"></a>
<FONT color="green">070</FONT>             * Constructor<a name="line.70"></a>
<FONT color="green">071</FONT>             * @param ctrl The Qubit in the Quantum register to act as the Control - decide if the target has to be changed.<a name="line.71"></a>
<FONT color="green">072</FONT>             * @param target The Qubit in the Quantum register to act as the Target - the Qubit that will change from 0 - 1.<a name="line.72"></a>
<FONT color="green">073</FONT>             */<a name="line.73"></a>
<FONT color="green">074</FONT>            protected CnotMatrix(int ctrl, int target){<a name="line.74"></a>
<FONT color="green">075</FONT>    <a name="line.75"></a>
<FONT color="green">076</FONT>                    /* Make sure the ctrl and target are not set to the same bit.<a name="line.76"></a>
<FONT color="green">077</FONT>                     * This is not allowed.<a name="line.77"></a>
<FONT color="green">078</FONT>                     */<a name="line.78"></a>
<FONT color="green">079</FONT>                    if(ctrl==target){<a name="line.79"></a>
<FONT color="green">080</FONT>                            throw new IllegalArgumentException("ERROR: Cnot cannot be applied with equal Control and Target bits.");<a name="line.80"></a>
<FONT color="green">081</FONT>                    }<a name="line.81"></a>
<FONT color="green">082</FONT>    <a name="line.82"></a>
<FONT color="green">083</FONT>                    // Set ctrl and target so it can be used in apply.<a name="line.83"></a>
<FONT color="green">084</FONT>                    this.ctrl = ctrl;<a name="line.84"></a>
<FONT color="green">085</FONT>                    this.target = target;<a name="line.85"></a>
<FONT color="green">086</FONT>    <a name="line.86"></a>
<FONT color="green">087</FONT>                    /*<a name="line.87"></a>
<FONT color="green">088</FONT>                     * Set all the constant matrices and values to be used within<a name="line.88"></a>
<FONT color="green">089</FONT>                     * the Gate. <a name="line.89"></a>
<FONT color="green">090</FONT>                     */<a name="line.90"></a>
<FONT color="green">091</FONT>                    num1 = new Complex(1.0,0.0);<a name="line.91"></a>
<FONT color="green">092</FONT>    <a name="line.92"></a>
<FONT color="green">093</FONT>                    outer_0 = new Matrix(2,2,0.0);<a name="line.93"></a>
<FONT color="green">094</FONT>                    outer_0.setElement(0, 0, num1);<a name="line.94"></a>
<FONT color="green">095</FONT>                    outer_1 = new Matrix(2,2,0.0);<a name="line.95"></a>
<FONT color="green">096</FONT>                    outer_1.setElement(1,1,num1);<a name="line.96"></a>
<FONT color="green">097</FONT>    <a name="line.97"></a>
<FONT color="green">098</FONT>                    Not = new Matrix(2,2,0.0);<a name="line.98"></a>
<FONT color="green">099</FONT>                    Not.setElement(0,1,num1);<a name="line.99"></a>
<FONT color="green">100</FONT>                    Not.setElement(1,0,num1);<a name="line.100"></a>
<FONT color="green">101</FONT>    <a name="line.101"></a>
<FONT color="green">102</FONT>                    /* Check special values of ctrl and target (the first Qubit) and if this is<a name="line.102"></a>
<FONT color="green">103</FONT>                     * the case, set the corresponding initial values.<a name="line.103"></a>
<FONT color="green">104</FONT>                     * If the ctrl is 0, the outer product must be constructed at the <a name="line.104"></a>
<FONT color="green">105</FONT>                     * beginning of the tensor products for each side of the matrix addition.<a name="line.105"></a>
<FONT color="green">106</FONT>                     * If the target is 0, the Not matrix must be at the beginning of the <a name="line.106"></a>
<FONT color="green">107</FONT>                     * RightHandSide tensor product.<a name="line.107"></a>
<FONT color="green">108</FONT>                     */<a name="line.108"></a>
<FONT color="green">109</FONT>                    if (ctrl==0){<a name="line.109"></a>
<FONT color="green">110</FONT>                            LHS = outer_0;<a name="line.110"></a>
<FONT color="green">111</FONT>                            RHS = outer_1;<a name="line.111"></a>
<FONT color="green">112</FONT>                    }<a name="line.112"></a>
<FONT color="green">113</FONT>                    else if (target==0){<a name="line.113"></a>
<FONT color="green">114</FONT>                            LHS = I2;<a name="line.114"></a>
<FONT color="green">115</FONT>                            RHS = Not;<a name="line.115"></a>
<FONT color="green">116</FONT>                    }<a name="line.116"></a>
<FONT color="green">117</FONT>                    else{<a name="line.117"></a>
<FONT color="green">118</FONT>                            LHS = I2;<a name="line.118"></a>
<FONT color="green">119</FONT>                            RHS = I2;<a name="line.119"></a>
<FONT color="green">120</FONT>                    }<a name="line.120"></a>
<FONT color="green">121</FONT>    <a name="line.121"></a>
<FONT color="green">122</FONT>            }<a name="line.122"></a>
<FONT color="green">123</FONT>    <a name="line.123"></a>
<FONT color="green">124</FONT>            /** The apply method which will allow the Gate to be appied to the Register.<a name="line.124"></a>
<FONT color="green">125</FONT>             * @param r The Quantum Register<a name="line.125"></a>
<FONT color="green">126</FONT>             */<a name="line.126"></a>
<FONT color="green">127</FONT>            public void apply(Register r) {<a name="line.127"></a>
<FONT color="green">128</FONT>                    // Find the length of the Quantum Register<a name="line.128"></a>
<FONT color="green">129</FONT>                    int numQubits = r.getNumQbits(); <a name="line.129"></a>
<FONT color="green">130</FONT>    <a name="line.130"></a>
<FONT color="green">131</FONT>                    /* Check to make sure the register is of adequate size for <a name="line.131"></a>
<FONT color="green">132</FONT>                     * the gate to be applied to. If not throw exception<a name="line.132"></a>
<FONT color="green">133</FONT>                     */<a name="line.133"></a>
<FONT color="green">134</FONT>                    if(numQubits&lt;2){<a name="line.134"></a>
<FONT color="green">135</FONT>                            throw new noQubitException("ERROR: Cnot can only be applied to a Quantum Register with =&gt; 2 Quantum Bits.");<a name="line.135"></a>
<FONT color="green">136</FONT>                    }<a name="line.136"></a>
<FONT color="green">137</FONT>                    <a name="line.137"></a>
<FONT color="green">138</FONT>                    if (target &gt;= r.getNumQbits() || target &lt; 0){<a name="line.138"></a>
<FONT color="green">139</FONT>                            throw new IllegalArgumentException("Target qubit not in register. Register size (qubits): " + r.getNumQbits() + " Target qubit: " + target);<a name="line.139"></a>
<FONT color="green">140</FONT>                    }<a name="line.140"></a>
<FONT color="green">141</FONT>                    <a name="line.141"></a>
<FONT color="green">142</FONT>                    if (ctrl &gt;= r.getNumQbits() || ctrl &lt; 0){<a name="line.142"></a>
<FONT color="green">143</FONT>                            throw new IllegalArgumentException("Control qubit not in register. Register size (qubits): " + r.getNumQbits() + " Control qubit: " + ctrl);<a name="line.143"></a>
<FONT color="green">144</FONT>                    }<a name="line.144"></a>
<FONT color="green">145</FONT>    <a name="line.145"></a>
<FONT color="green">146</FONT>                    /* Since the initial steps have already been set in the Gate constructor<a name="line.146"></a>
<FONT color="green">147</FONT>                     * which depend on the specific ctrl and target set, we then loop over the<a name="line.147"></a>
<FONT color="green">148</FONT>                     * remaining number of Qubits in the register to either set the position<a name="line.148"></a>
<FONT color="green">149</FONT>                     * of our outer products or the position for the Not matrix. The loop<a name="line.149"></a>
<FONT color="green">150</FONT>                     * will then build up both the LHS and RHS so they can then be added and <a name="line.150"></a>
<FONT color="green">151</FONT>                     * applied to the register.<a name="line.151"></a>
<FONT color="green">152</FONT>                     */<a name="line.152"></a>
<FONT color="green">153</FONT>                    for (int i=1; i&lt;numQubits;i++){<a name="line.153"></a>
<FONT color="green">154</FONT>                            if(i==ctrl){<a name="line.154"></a>
<FONT color="green">155</FONT>                                    LHS = LHS.tensorProduct(outer_0);<a name="line.155"></a>
<FONT color="green">156</FONT>                                    RHS = RHS.tensorProduct(outer_1);<a name="line.156"></a>
<FONT color="green">157</FONT>                            }<a name="line.157"></a>
<FONT color="green">158</FONT>                            else if(i==target){<a name="line.158"></a>
<FONT color="green">159</FONT>                                    LHS = LHS.tensorProduct(I2);<a name="line.159"></a>
<FONT color="green">160</FONT>                                    RHS = RHS.tensorProduct(Not);<a name="line.160"></a>
<FONT color="green">161</FONT>                            }<a name="line.161"></a>
<FONT color="green">162</FONT>                            else{<a name="line.162"></a>
<FONT color="green">163</FONT>                                    LHS = LHS.tensorProduct(I2);<a name="line.163"></a>
<FONT color="green">164</FONT>                                    RHS = RHS.tensorProduct(I2);<a name="line.164"></a>
<FONT color="green">165</FONT>                            }<a name="line.165"></a>
<FONT color="green">166</FONT>                    }<a name="line.166"></a>
<FONT color="green">167</FONT>    <a name="line.167"></a>
<FONT color="green">168</FONT>                    // Add LHS &amp; RHS and apply matrix to the register and update.<a name="line.168"></a>
<FONT color="green">169</FONT>                    Matrix result = RHS.addMatrix(LHS);     <a name="line.169"></a>
<FONT color="green">170</FONT>                    r.update(result.multiplyMatrix(r));<a name="line.170"></a>
<FONT color="green">171</FONT>            }<a name="line.171"></a>
<FONT color="green">172</FONT>    <a name="line.172"></a>
<FONT color="green">173</FONT>    <a name="line.173"></a>
<FONT color="green">174</FONT>            /**<a name="line.174"></a>
<FONT color="green">175</FONT>             *  Return the name of the matrix.<a name="line.175"></a>
<FONT color="green">176</FONT>             */<a name="line.176"></a>
<FONT color="green">177</FONT>            public String getName() {<a name="line.177"></a>
<FONT color="green">178</FONT>                    return "Cnot";<a name="line.178"></a>
<FONT color="green">179</FONT>            }<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>    }<a name="line.181"></a>




























































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